Handbook of Categorical Algebra

A Handbook of Categorical Algebra in three volumes is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. After introducing the terminology and proving the fundamental results concerning limits adjoint functors and Kan extensions the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various refinements of the fundamental concepts of category and functor.